This project will examine new methodology for important issues in the analysis of censored failure time data. The methodology addresses problems occurring frequently in clinical investigations for chronic diseases, including cancer and AIDS. The specific objectives of the project are to: 1. Develop and study nonparametric methods for incorporating information on disease progression in the analysis of survival, to improve the efficiency of estimates and tests. An example where this would be useful is in clinical trials for adjuvant breast cancer therapy. At times of analysis there will usually be a substantial number of patients who have relapsed but are still alive, so incorporating information on recurrence should improve the analysis of survival. 2. Explore methods for modeling the distribution of times between repeated events. There are many models of varying complexity that can be used for multiple event data. This project will explore the effect on bias and efficiency from using incorrect models, and investigate tests for discriminating among models. 3. Develop methods for regression analysis of censored failure time data with partially missing information on covariates. Partially missing covariate data is a frequent problem in biomedical research. Both semi-parametric methods which involve finding unbiased estimating equations, and Bayesian methods which require full specification of the joint distributions, will be investigated. 4. Investigate methodology for detecting and estimating treatment by institution interactions in multi-center clinical trials. Large phase III trials of cancer therapy usually include patients from many hospitals and clinics. In this project treatment differences for individual institutions will be modeled as random effects. Overall tests for treatment by institution interactions, and Bayesian methods for estimating the treatment effects, will both be investigated.